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Serenitypaige1129
Group Title
What is a quartic function with only the two real zeroes given?
x = –1 and x = –3
 one year ago
 one year ago
Serenitypaige1129 Group Title
What is a quartic function with only the two real zeroes given? x = –1 and x = –3
 one year ago
 one year ago

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tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
You can go with (x + 1)^2 times (x + 3)^2 The reason this works is that it will give you a x^4 term and you still have only the 2 roots. Roots are of the form: (x  root) for you factors.
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
So, basically you have both roots twice, so that's why each factor has a 2 on it for an exponent.
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
You could also have put a 3 on one of them and left the other root as a single power (no exponent)
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
Is this making sense to you?
 one year ago

Serenitypaige1129 Group TitleBest ResponseYou've already chosen the best response.0
I am lost completely
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
np, I'll give you a little more detail: First off, a quartic polynomial function has as its highest exponent, an x^4 term. That means that if you have an equation of the form: y = (x  root1)(x  root2)(x  root3)(x  root4) you will have quartic function. But we can have only 2 different roots, so a good choice is to have root1 twice and root 2 twice: y = [(x  root1)^2][(x  root2)^2]
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
That's the same as: y = (x  root1)(x  root1)(x  root2)(x  root2) which also has root1 twice and root2 twice. It's just writing out the factors without the exponents. This equation will give you 0 for "y" if you replace x with either root, which is what you want to solve this problem.
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
And to finish this off, you are given x = 1 and x = 3 as the only 2 roots you can have. And since the factor to give "0" using the root is: (x  root) one factor is [x  (1)] which is (x + 1) the other is [x  (3)] which is (x + 3) So, your polynomial is: y = (x + 1)(x + 1)(x + 3)(x + 3)
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
You have other choices, but the above polynomial works. You could also have: y = (x + 1)(x + 3)(x + 3)(x + 3) or y = (x + 1)(x + 1)(x + 1)(x + 3) Both of those are quartics having only 2 different roots. That should make it all clearer now. Now are you good on this?
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
Here's a graph of the first solution
 one year ago

Serenitypaige1129 Group TitleBest ResponseYou've already chosen the best response.0
sorta so which one would it be? y = x4 – 4x3 – 4x2 – 4x – 3 y = –x4 + 4x3 + 4x2 + 4x + 3 y = x4 + 4x3 + 3x2 + 4x – 4 y = x4 + 4x3 + 4x2 + 4x +3 I understand how you did that i just don't know which one it will be.
 one year ago

Serenitypaige1129 Group TitleBest ResponseYou've already chosen the best response.0
@tcarroll010
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
I didn't know that you had choices. That changes the whole way you approach this problem. You can solve it 2 ways that I know of. The first way rst and the best and fastest is to perfrom synthetic division on each choice until you hit upon the choice that has only those 2 roots.
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
Number #1 is out because 1 is not a root. So, I eliminated that one so far.
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
Number 2 is out because it also has +1 as a root.
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
Are you sure you wrote those choices down correctly?
 one year ago

Serenitypaige1129 Group TitleBest ResponseYou've already chosen the best response.0
I actually copied and paste so yeah
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
And the roots are supposed to be 1 and 3 ?
 one year ago

Serenitypaige1129 Group TitleBest ResponseYou've already chosen the best response.0
yeah that is why i couldn't figure it out. That is what confused me
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
It looks like like the last one works. I tried it again.
 one year ago

Serenitypaige1129 Group TitleBest ResponseYou've already chosen the best response.0
okay thanks again
 one year ago

tcarroll010 Group TitleBest ResponseYou've already chosen the best response.1
you're welcome.
 one year ago
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